Sufficiently Homogeneous Closed Embeddings of An-1 into An are Linear
Canadian journal of mathematics, Tome 48 (1996) no. 6, pp. 1286-1295

Voir la notice de l'article provenant de la source Cambridge University Press

We show that over a field k of characteristic zero an affine (n — 1)- space embedded as a closed subvariety in affine n-space and homogeneous for a codimension two linear torus action on is defined by the vanishing of a variable.
DOI : 10.4153/CJM-1996-068-8
Mots-clés : 14E25, 14E09
Russell, Peter. Sufficiently Homogeneous Closed Embeddings of An-1 into An are Linear. Canadian journal of mathematics, Tome 48 (1996) no. 6, pp. 1286-1295. doi: 10.4153/CJM-1996-068-8
@article{10_4153_CJM_1996_068_8,
     author = {Russell, Peter},
     title = {Sufficiently {Homogeneous} {Closed} {Embeddings} of {An-1} into {An} are {Linear}},
     journal = {Canadian journal of mathematics},
     pages = {1286--1295},
     year = {1996},
     volume = {48},
     number = {6},
     doi = {10.4153/CJM-1996-068-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-068-8/}
}
TY  - JOUR
AU  - Russell, Peter
TI  - Sufficiently Homogeneous Closed Embeddings of An-1 into An are Linear
JO  - Canadian journal of mathematics
PY  - 1996
SP  - 1286
EP  - 1295
VL  - 48
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-068-8/
DO  - 10.4153/CJM-1996-068-8
ID  - 10_4153_CJM_1996_068_8
ER  - 
%0 Journal Article
%A Russell, Peter
%T Sufficiently Homogeneous Closed Embeddings of An-1 into An are Linear
%J Canadian journal of mathematics
%D 1996
%P 1286-1295
%V 48
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-068-8/
%R 10.4153/CJM-1996-068-8
%F 10_4153_CJM_1996_068_8

[A] [A] Abhyankar, S. S., Expansion Techniques in Algebraic Geometry, Tata Institute of Fundamental Research, Lecture Notes on Mathematics and Physics, Bombay (1977). Google Scholar

[AM] [AM] Abhyankar, S. S. and Moh, T.-T., Embeddings of the line in the plane, J. Reine Angew. Math. 276(1975), 148–166. Google Scholar

[B-B] [B-B] Bialynicki-Birula, A., Remarks on the action of an algebraic torus on kn, and , Bull. Acad. Pol. Sci. 14(1966), 177–181 and 15(1967), 123-125. Google Scholar

[BH] [BH] Bass, H. and Haboush, W., Linearizing certain reductive group actions, Trans. Am. Math. Soc. (2)292 (1985), 463–481. Google Scholar

[KbR] [KbR] Kambayashi, T. and Russell, P., On linearizing algebraic torus actions, J. Pure Appl. Algebra 23(1982), 243–250. Google Scholar

[KR1] [KR1] Koras, M. and Russell, P., On linearizing “good” C*-actions on C3, Can. Math. Soc. Conf. Proc. 10 (1989), 92–102. Google Scholar

[KR2] [KR2] Koras, M. and Russell, P., Codimension 2 torus actions on affine n-space, Canad. Math. Soc. Conf. Proc. 10(1989), 103—110. Google Scholar

[KR3] [KR3] Koras, M. and Russell, P., Contractible threefolds and C*-actions on C3 , manuscript, CICMA preprint series. Google Scholar

[KR4] [KR4] Koras, M. and Russell, P., On C3/C*; the smooth locus is not of hyperbolic type, in preparation. Google Scholar

[PTD] [PTD] Petrie, T. and Tom Dieck, T., The Abhyankar-Moh problem in dimension 3, Springer Lecture Notes in Mathematics 1375(1989), 48–59. Google Scholar

[RS] [RS] Russell, P. and Sathaye, A., Onfinding and cancelling variables in k[X, Y,Z], J. Alg. (1)57(1979), 151–166. Google Scholar

[S] [S] Suzuki, M., Propriétés topologiques des polynomes de deux variables complexes et automorphismes algébriques de Vespace C2, J. Math. Soc. Japan 26(1974), 241–257. Google Scholar

Cité par Sources :